Table Of Contents
219 LearnersLast updated on November 30th, 2024
Cube Root of 243
The cube root of 243 is the value that, when multiplied by itself three times (cubed), gives the original number 243. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, designing structures, density and mass, field of engineering etc.
What Is the Cube Root of 243?
The cube root of 243 is 6.24025146916. The cube root of 243 is expressed as β243 in radical form, where the β β β sign is called the βradicalβ sign. In exponential form, it is written as (243)1/3. If βmβ is the cube root of 243, then, m3=243. Let us find the value of βmβ.
Finding the Cube Root of 243
The cube root of 243 is expressed as 3β9 as its simplest radical form, since
243 = 3Γ3Γ3Γ3Γ3
β243 = β(3Γ3Γ3Γ3Γ3)
Group together three same factors at a time and put the remaining factor under β .
β243= 3β9
We can find cube root of 243 through a method, named as, Halleyβs Method. Let us see how it finds the result.
Cube Root of 243 By Halleyβs Method
Now, what is Halleyβs Method?
It is an iterative method for finding cube roots of a given number N, such that, x3=N, where this method approximates the value of βxβ.
Formula is βaβ
x((x3+2a) / (2x3+a)), where
a=given number whose cube root you are going to find
x=integer guess for the cubic root
Let us apply Halleyβs method on the given number 243.
Step 1: Let a=243. Let us take x as 6, since, 63=216 is the nearest perfect cube which is less than 243.
Step 2: Apply the formula. β243β
6((63+2Γ243) / (2(6)3+243))= 6.24
Hence, 6.24 is the approximate cubic root of 243.
Common Mistakes and How to Avoid Them in the Cube Root of 243
some common mistakes and solutions are given below:
Mistake 1
Students might guess the cube root by rounding to the nearest number, leading to inaccuracy. For β216, the student might mistakenly think the answer is 5, where 63
Donβt round off to the nearest number and find cube roots, it is advisable to use proper methods to find cube roots.
Cube Root of 243 Examples
Problem 1
Find (β240/ β243) Γ (β241/ β243) Γ (β242/ β243)
(β240/ β243) Γ (β241/ β243) Γ (β242/ β243)
= (β240Γ β241Γ β242) / (β243Γ β243Γ β243)
=(β240Γ β241Γ β242)/ ((243)β
)3
=(β240Γ β241Γ β242)/243
=(6.214 Γ 6.223 Γ 6.231)/ 243
Answer: (6.214 Γ 6.223 Γ 6.231)/ 243
Explanation
We used the fact that ((243)β
)3=243 and then found the cube roots of 240,241, and 242 and simplified.
Problem 2
The length, breadth, and height of a cuboid is 5 unit, 4 unit, and 4.5 cm respectively. To find its volume, also find the measure of a side of a cube, whose volume is 243 cubic units.
Volume of a cuboid = length Γ breadth Γ height = 5 Γ 4 Γ 4.5 cubic units = 90 cubic units.
Given, Volume of a cube = 243 cubic units
β side Γ side Γ side = 243 cubic units
β side = β243
β side = 6.24 units
Answer: Volume of the cuboid = 90 cubic units
Side length of the cube = 6.24 units
Explanation
Applied the formula and concept of the volume of a cuboid and cube and solved.
Problem 3
Multiply β243 Γ β216
β243Γβ216
= 6.24Γ6
= 37.44
Answer: 37.44
Explanation
We know that the cubic root of 216 is 6, hence multiplying β216 with β243.
Problem 4
What is β(243βΆ^1/6) ?
β(2436Γ1/6)
= (243)1/3
= 6.24β¦
Answer: 6.24
Explanation
We solved and simplified the exponent part first using the fact that, (2436Γ1/6)=243, then solved.
Problem 5
Find β(243-(-100)).
β(243-(-100))
= β(243+100)
=β343
=7
Answer: 7
Explanation
Simplified the expression, and found out the cubic root of the result.
FAQs on 243 Cube Root
1.What are perfect cube factors are included in 243?
2.Is 243 a perfect square?
3.What are the factors of 243?
4.Which power of 3 is 243?
5.What is 243 divisible by?
Important Glossaries for Cube Root of 243
- Integers - Integers can be a positive natural number, negative of a positive number, or zero. We can perform all the arithmetic operations on integers. The examples of integers are, 1, 2, 5,8, -8, -12, etc.
- Whole numbers - The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity.
- Square root -The square root of a number is a value βyβ such that when βyβ is multiplied by itself β y Γ y, the result is the original number.
- Polynomial - It is an algebraic expression made up of variables like βxβ and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.
- Approximation - Finding out a value which is nearly correct, but not perfectly correct.
- Iterative method - This method is a mathematical process which uses an initial value to generate further and step-by-step sequence of solutions for a problem.
Explore More algebra
Previous to Cube Root of 243
Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
